RECOMBINATION IN SEXUAL ORGANISMS 65 



must also be linked to thi. When the 6884 gametes studied in these 

 crosses were examined for the combinations of arg and thi genes, it was 

 found that 43 per cent contained new combinations. This frequency, 

 because of the large number of gametes studied, is also significantly 

 different from 50 per cent, so we must conclude that arg and thi are also 

 linked, even if less strongly. Thus we know that arg, paba, and thi are 

 linked and tend to pass into the gametes in parental association, what- 

 ever that association may be in a particular cross. 



In addition to this case of linkage in Chlamydomonas, we have already 

 seen another in pneumococcus. The factors str-r and mtl showed linkage 

 in transformation. In the genetic studies of all organisms, it is found 

 that some factor pairs recombine freely whereas others undergo re- 

 stricted recombination yielding recombinants in frequencies varying from 

 0.0 to 0.5, the actual value being characteristic of the allelic pairs. 



The fact of linkage suggests that genes are arranged as parts of some 

 cell structure. Because recombination takes place, linkage is not com- 

 plete; exchange of genetic material occurs with a frequency that must be 

 a function of the particular physical association between two given genes. 

 In a purely formal way, we can draw some conclusions about this physi- 

 cal association, using the results of recombination alone. For example, 

 it is possible to show that genes are arranged in a linear order and to 

 make a map of their sequence. 



The principle is very simple. We will illustrate it by an example with 

 which everyone is familiar and, once again, we will use rain as a source 

 of random events. Consider a clothes line marked off into two segments, 

 one being half the length of the other. When exposed to a shower, the 

 longer one will, on the average, be hit by raindrops twice as often as the 

 shorter. Of course, the absolute number of hits will depend upon the 

 density of the rain, the length of the shower, and the thickness of the 

 line. But the relative number of hits is actually a measure of segment 

 length. If we found that one segment were hit twice as often as the 

 other, we would judge it to be twice as long. The point separating the 

 two segments is x hits from one end of the line and 2jc hits away from 

 the other end when the total number of hits on the line is recorded as 3.v. 



With this analogy in mind, we may ask whether the distance between 

 two genes determines the amount of recombination between them. If re- 

 combinations occur between the genes arg and paba 15 per cent of the 

 time, and between genes paba and thi 30 per cent of the time, we would 

 suppose the distance between arg and paba to be half the distance be- 

 tween paba and thi. But we would not know whether they were ar- 

 ranged in a linear order, as three points on a surface, or in a three- 



